A rabbit runs in a straight line with a velocity of +1.3 m/s for a period of time, rests for 11 s, and then runs again along the same line at +0.65 m/s for an unknown amount of time. The rabbit travels a total distance of 1080 m, and its average speed is 0.79 m/s.What is the total time the rabbit spends running at 1.3m/s. Please help me im not sure if I am doing this correctly I just need to see what equation to use and steps on how I go into figuring this out.
To find the total time the rabbit spends running at 1.3 m/s, we can follow these steps:
Step 1: Determine the total time the rabbit spent running at 1.3 m/s
Let's assume the rabbit spent t1 seconds running at 1.3 m/s.
Step 2: Determine the time the rabbit spent resting
The rabbit spent 11 seconds resting.
Step 3: Determine the total time the rabbit spent running at 0.65 m/s
Let's assume the rabbit spent t2 seconds running at 0.65 m/s.
Step 4: Determine the equation for distance traveled
The total distance traveled by the rabbit can be calculated by adding the distance traveled in each phase:
Distance1 + Distance2 = 1080 m
Step 5: Write an equation for the total time spent running
Based on the given information, we can write the equation:
t1 + 11 s + t2 = total time
Step 6: Write an equation for the average speed
The average speed is given as 0.79 m/s. Average speed can be calculated using the formula:
Average speed = total distance / total time
Step 7: Solve for the equations and find the total time
Using the equations from step 5 and step 6, substitute the known values into the equations and solve for the unknowns (t1, t2).
By following these steps, you should be able to find the total time the rabbit spends running at 1.3 m/s.
To find the total time the rabbit spends running at 1.3 m/s, let's break down the problem:
1. Let's assume the rabbit runs at 1.3 m/s for time 't1' and at 0.65 m/s for time 't2'.
2. We know that the rabbit rests for 11 seconds, so the equation becomes:
Distance at 1.3 m/s + Distance at 0.65 m/s = Total Distance
(1.3 m/s * t1) + (0.65 m/s * t2) = 1080 m ----(equation 1)
3. We are given that the average speed is 0.79 m/s, which we can calculate using the formula:
Average speed = Total distance / Total time
0.79 m/s = 1080 m / Total time ----(equation 2)
4. Rearranging equation 2, we get:
Total time = 1080 m / 0.79 m/s = 1367.09 s
Now, we have two variables 't1' and 't2' and two equations (equation 1 and equation 2). We can solve these equations simultaneously to find the value of 't1', which represents the total time the rabbit spends running at 1.3 m/s.
Solving the equations:
From equation 1, we can isolate 't1':
1.3t1 + 0.65t2 = 1080 m
To solve for 't1', let's express 't2' in terms of 't1' and substitute it into equation 1:
t2 = 1367.09 s - t1 (from equation 2)
Substituting in equation 1:
1.3t1 + 0.65(1367.09 s - t1) = 1080 m
Simplifying the equation:
1.3t1 + 889.71 s - 0.65t1 = 1080 m
0.65t1 + 889.71 s = 1080 m
Subtracting 889.71 s from both sides of the equation:
0.65t1 = 1080 m - 889.71 s
0.65t1 = 190.29 m
Dividing both sides of the equation by 0.65:
t1 = 190.29 m / 0.65 = 292.6 s
Therefore, the rabbit spends a total of approximately 292.6 seconds (s), or 4 minutes and 52.6 seconds (min:sec) running at 1.3 m/s.